skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants

Abstract

The few determinant (FED) methodology, introduced in our previous works for 1D lattices, is here adapted for the repulsive two-dimensional Hubbard model at half-filling and with finite doping fractions. Within this configuration mixing scheme, a given ground state with well defined spin and space group quantum numbers, is expanded in terms of a nonorthogonal symmetry-projected basis determined through chains of variation-after projection calculations. The results obtained for the ground state and correlation energies of half-filled and doped 4×4, 6×6, 8×8, and 10×10 lattices, as well as momentum distributions and spin-spin correlation functions in small lattices, compare well with those obtained using other state-of-the-art approximations. The structure of the intrinsic determinants resulting from the variational strategy is interpreted in terms of defects that encode information on the basic units of quantum fluctuations in the considered 2D systems. The varying nature of the underlying quantum fluctuations, reflected in a transition to a stripe regime for increasing onsite repulsions, is discussed using the intrinsic determinants belonging to a 16×4 lattice with 56 electrons. Such a transition is further illustrated by computing spin-spin and charge-charge correlation functions with the corresponding multireference FED wave functions. In good agreement with previous studies, the analysis of themore » pairing correlation functions reveals a weak enhancement of the extended s-wave and $$d_x2-_y2$$ pairing modes. Finally, given the quality of results here reported together with those previously obtained for 1D lattices and the parallelization properties of the FED scheme, we believe that symmetry projection techniques are very well suited for building ground state wave functions of correlated electronic systems, regardless of their dimensionality.« less

Authors:
 [1];  [2];  [3]
  1. Rice Univ., Houston, TX (United States). Dept. of Chemistry; Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy
  2. Rice Univ., Houston, TX (United States). Dept. of Chemistry
  3. Rice Univ., Houston, TX (United States). Dept. of Chemistry; Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Univ. of California, Oakland, CA (United States); Rice Univ., Houston, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1565362
Alternate Identifier(s):
OSTI ID: 1179903
Grant/Contract Number:  
AC02-05CH11231; SC0001474; FG02-09ER16053
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 90; Journal Issue: 19; Journal ID: ISSN 1098-0121
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics

Citation Formats

Rodríguez-Guzmán, R., Jiménez-Hoyos, Carlos A., and Scuseria, Gustavo E. Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants. United States: N. p., 2014. Web. doi:10.1103/PhysRevB.90.195110.
Rodríguez-Guzmán, R., Jiménez-Hoyos, Carlos A., & Scuseria, Gustavo E. Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants. United States. https://doi.org/10.1103/PhysRevB.90.195110
Rodríguez-Guzmán, R., Jiménez-Hoyos, Carlos A., and Scuseria, Gustavo E. 2014. "Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants". United States. https://doi.org/10.1103/PhysRevB.90.195110. https://www.osti.gov/servlets/purl/1565362.
@article{osti_1565362,
title = {Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants},
author = {Rodríguez-Guzmán, R. and Jiménez-Hoyos, Carlos A. and Scuseria, Gustavo E.},
abstractNote = {The few determinant (FED) methodology, introduced in our previous works for 1D lattices, is here adapted for the repulsive two-dimensional Hubbard model at half-filling and with finite doping fractions. Within this configuration mixing scheme, a given ground state with well defined spin and space group quantum numbers, is expanded in terms of a nonorthogonal symmetry-projected basis determined through chains of variation-after projection calculations. The results obtained for the ground state and correlation energies of half-filled and doped 4×4, 6×6, 8×8, and 10×10 lattices, as well as momentum distributions and spin-spin correlation functions in small lattices, compare well with those obtained using other state-of-the-art approximations. The structure of the intrinsic determinants resulting from the variational strategy is interpreted in terms of defects that encode information on the basic units of quantum fluctuations in the considered 2D systems. The varying nature of the underlying quantum fluctuations, reflected in a transition to a stripe regime for increasing onsite repulsions, is discussed using the intrinsic determinants belonging to a 16×4 lattice with 56 electrons. Such a transition is further illustrated by computing spin-spin and charge-charge correlation functions with the corresponding multireference FED wave functions. In good agreement with previous studies, the analysis of the pairing correlation functions reveals a weak enhancement of the extended s-wave and $d_x2-_y2$ pairing modes. Finally, given the quality of results here reported together with those previously obtained for 1D lattices and the parallelization properties of the FED scheme, we believe that symmetry projection techniques are very well suited for building ground state wave functions of correlated electronic systems, regardless of their dimensionality.},
doi = {10.1103/PhysRevB.90.195110},
url = {https://www.osti.gov/biblio/1565362}, journal = {Physical Review. B, Condensed Matter and Materials Physics},
issn = {1098-0121},
number = 19,
volume = 90,
place = {United States},
year = {Fri Nov 07 00:00:00 EST 2014},
month = {Fri Nov 07 00:00:00 EST 2014}
}

Journal Article:

Citation Metrics:
Cited by: 11 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Microscopic description of fission in uranium isotopes with the Gogny energy density functional
journal, May 2014


Theory of Resonating Quantum Fluctuations in a Fermion System: Resonating Hartree-Fock Approximation
journal, September 1988


On the limited memory BFGS method for large scale optimization
journal, August 1989


Many-body physics with ultracold gases
journal, July 2008


Quantum Fluctuations due to Spinons, Polarons, and Stripes in the Two-Dimensional Hubbard Model
journal, September 2009


Spin and Charge Order in the Doped Hubbard Model: Long-Wavelength Collective Modes
journal, March 2010


Nuclear structure theory in spin- and number-conserving quasiparticle configuration spaces: General formalism
journal, January 1984


Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory
journal, November 2012


Numerical study of the two-dimensional Hubbard model
journal, July 1989


Two-Dimensional Hubbard Model –Metal Insulator Transition Studied by Monte Carlo Calculation–
journal, September 1992


Iron-Based Layered Superconductor La[O 1- x F x ]FeAs ( x = 0.05−0.12) with T c = 26 K
journal, March 2008


Multi-component symmetry-projected approach for molecular ground state correlations
journal, November 2013


N -electron Slater determinants from nonunitary canonical transformations of fermion operators
journal, November 2012


Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
journal, January 2014


Fermionic projected entangled pair states
journal, May 2010


Electron correlation in solids via density embedding theory
journal, August 2014


Density matrix formulation for quantum renormalization groups
journal, November 1992


Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
journal, December 2009


Correlations beyond the mean field in magnesium isotopes: angular momentum projection and configuration mixing
journal, October 2002


Two-dimensional Hubbard model: Numerical simulation study
journal, April 1985


Self-energy-functional approach to systems of correlated electrons
journal, April 2003


Resonating Hartree-Fock Theory of the One DimensionalHubbard Model. I.Quantum Fluctuations by SDW Solitons and Breathers
journal, October 1991


The electronic properties of graphene
journal, January 2009


Resonating Hartree-Fock Theory of the One Dimensional Hubbard Model. II. Breather Fluctuations in the Strong Correlation Regime
journal, September 1992


Potential energy curves for Mo 2 : multi-component symmetry-projected Hartree–Fock and beyond
journal, January 2014


Dynamical cluster approximation employing the fluctuation exchange approximation as a cluster solver
journal, February 2003


Direct evidence for a gapless Z 2 spin liquid by frustrating Néel antiferromagnetism
journal, August 2013


Phase diagram of a frustrated Heisenberg antiferromagnet on the honeycomb lattice: The J 1 - J 2 - J 3 model
journal, October 2012


Complexity in Strongly Correlated Electronic Systems
journal, July 2005


Symmetry-projected variational approach to the one-dimensional Hubbard model
journal, August 2005


The density-matrix renormalization group
journal, April 2005


Symmetry in auxiliary-field quantum Monte Carlo calculations
journal, September 2013


Antiferromagnetism in the Two-Dimensional Hubbard Model
journal, January 1989


Correlated electrons in high-temperature superconductors
journal, July 1994


Intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
journal, April 2014


Correlations in the two-dimensional Hubbard model
journal, April 1991


Optical conductivity of the Hubbard and t - J models
journal, September 1990


Exploring Copper Oxide Cores Using the Projected Hartree–Fock Method
journal, September 2012


Excited electronic states from a variational approach based on symmetry-projected Hartree–Fock configurations
journal, December 2013


Symmetry-projected variational approach for ground and excited states of the two-dimensional Hubbard model
journal, June 2012


Distinct spinon and holon dispersions in photoemission spectral functions from one-dimensional SrCuO2
journal, May 2006


Pseudogaps in the 2D Hubbard Model
journal, January 2001


Multireference symmetry-projected variational approaches for ground and excited states of the one-dimensional Hubbard model
journal, June 2013


Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette
journal, March 1931


Group-theoretical and resonating Hartree-Fock studies for spin fluctuations in two-dimensional Hubbard model on triangular lattice
journal, December 2011


Small amplitude vibrations in symmetry-projected quasi-particle mean fields
journal, February 1989


Density matrix embedding from broken symmetry lattice mean fields
journal, January 2014


Orbital Optimization in the Resonating Hartree-Fock Approximation and Its Application to the One Dimensional Hubbard Model
journal, May 1993


Generalized coherent states and some of their applications
journal, September 1977


Static and dynamical properties of doped Hubbard clusters
journal, May 1992


Gaussian-Basis Monte Carlo Method for Numerical Study on Ground States of Itinerant and Strongly Correlated Electron Systems
journal, August 2007


Quantum cluster theories
journal, October 2005


Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet
journal, April 2011


Electron correlations in the two-dimensional Hubbard model: A group-theoretical and numerical study
journal, July 1992


Optical-conductivity properties of one-dimensional Hubbard rings: Repulsive- U and attractive- U cases
journal, April 1992


Multireference symmetry-projected variational approximation for the ground state of the doped one-dimensional Hubbard model
journal, May 2014


Giant thermoelectric Seebeck coefficient of a two-dimensional electron gas in SrTiO3
journal, January 2007


Optical Conductivity of the Half-Filled Hubbard Chain
journal, October 2000


Charge-spin separation and the spectral properties of Luttinger liquids
journal, March 1993


Missing Quasiparticles and the Chemical Potential Puzzle in the Doping Evolution of the Cuprate Superconductors
journal, December 2004


A cellular dynamical mean field theory approach to Mottness
journal, July 2006


The Density Matrix Renormalization Group in Quantum Chemistry
journal, May 2011


Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice
journal, December 2008


Superconductivity in iron compounds
journal, December 2011


Projected quasiparticle theory for molecular electronic structure
journal, September 2011


Striped phase in the cuprates as a semiclassical phenomenon
journal, April 1996


Evidence for stripe correlations of spins and holes in copper oxide superconductors
journal, June 1995


Frustrated Heisenberg antiferromagnet on the checkerboard lattice: J 1 - J 2 model
journal, May 2012


The density-matrix renormalization group in the age of matrix product states
journal, January 2011


Spin- and charge-density waves in the Hartree–Fock ground state of the two-dimensional Hubbard model
journal, November 2011


Unrestricted Hartree-Fock theory and its applications to molecules and chemical reactions
journal, November 1981


Absence of a Slater Transition in the Two-Dimensional Hubbard Model
journal, October 2001


Effect of Correlation on the Ferromagnetism of Transition Metals
journal, March 1963


Stripes on a 6-Leg Hubbard Ladder
journal, September 2003


Variational reduced-density-matrix calculation of the one-dimensional Hubbard model
journal, June 2006


Possible highT c superconductivity in the Ba?La?Cu?O system
journal, June 1986


Symmetry-projected wave functions in quantum Monte Carlo calculations
journal, March 2014


A Jacobi Equation on the Coset Manifold SO(2N)/U(N) and the Quasi-Particle RPA Equation
journal, January 1983


Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
journal, January 1996


Projected Hartree–Fock theory
journal, April 2012


Microscopic description of quadrupole-octupole coupling in Sm and Gd isotopes with the Gogny energy density functional
journal, September 2012


Electron correlations in narrow energy bands
journal, November 1963


Magnetism and its microscopic origin in iron-based high-temperature superconductors
journal, October 2012


Truncated configuration interaction expansions as solvers for correlated quantum impurity models and dynamical mean-field theory
journal, October 2012


A Mott insulator of fermionic atoms in an optical lattice
journal, September 2008


Global symmetries in tensor network states: Symmetric tensors versus minimal bond dimension
journal, September 2013


Stripe formation in doped Hubbard ladders
journal, February 2005


Works referencing / citing this record:

Hartree–Fock symmetry breaking around conical intersections
journal, January 2018


Efficient computation of matrix elements of generic Slater determinants
journal, January 2020


Efficient computation of matrix elements of generic Slater determinants
text, January 2019